jmc

Using the vertex and focus, we can see that the equation of the directrix must be $y=-1.$



Let $P=(x,y)$ be a point on the parabola. Then by definition of the parabola, $PF$ is equal to the distance from $P$ to the directrix, which is $y+1.$ Hence, $$\sqrt{x^2+(y-1{)}^2}=y+1.$$Squaring, we get $x^2+(y-1{)}^2=(y+1{)}^2.$ This simplifies to $x^2=4y.$

We are given that $PF=101,$ so $y+1=101,$ and hence $y=100.$ Then $x^2=400.$ Since the point is in the first quadrant, $x=20.$ Hence, $P=\boxed{(20,100)}.$